The Sum of Money Increases by 60 in 4 Years at Simple Interest: What is the Compound Interest for Rs. 20000 After 4 Years?

In financial mathematics, understanding the differences between simple and compound interest is essential for making informed investment decisions. This article delves into the calculations of these two types of interest, providing a clear explanation and practical examples.

Understanding Simple Interest

Simple interest is a type of interest that is calculated based on the principal amount, the rate of interest, and the time period. The formula for simple interest (SI) is given by:

SI (P times; R times; T) / 100

P represents the principal amount. R is the interest rate per annum. T is the time period in years.

Example Calculation

A sum of money increases by 60 in 4 years at simple interest. To find the rate of interest, let's assume the principal is Rs. 100. The interest earned is Rs. 60 in 4 years.

SI (100 times; R times; 4) / 100 60

Solving for R, we get:

4R 60

R 15%

Comparing Simple and Compound Interest

Now, let's consider the same principal amount (Rs. 20000) and calculate the compound interest (CI) after 4 years at the same rate of 15%.

Calculating Compound Interest

Compound interest is calculated using the formula:

CI P times; (1 R/100)^T - P

Here, P 20000, R 15, and T 4.

CI 20000 times; (1 15/100)^4 - 20000

CI 20000 times; (1.15)^4 - 20000

CI 20000 times; 1.74900625 - 20000

CI 34980.125 - 20000

CI 14980.125

Around the final step, rounding off the decimal is typically done to avoid compounding errors. Therefore, the compound interest is approximately Rs. 14980.10.

Rate of Interest Calculation

Let's summarize the rate of interest calculation. Given the increase in money is Rs. 60 in 4 years at simple interest, the rate of interest is calculated as:

R (Increase in amount / Time period) (60 / 4) 15%

Therefore, the rate of interest is 15% per annum.

Practical Example

Suppose we have an initial principal of Rs. 15000 and we want to find the compound interest after 4 years at a 15% interest rate.

CI 15000 times; (1 15/100)^4 - 15000

CI 15000 times; (1.15)^4 - 15000

CI 15000 times; 1.74900625 - 15000

CI 26235.09375 - 15000

CI 11235.09375

Therefore, the compound interest for Rs. 15000 after 4 years at a 15% interest rate is approximately Rs. 11235.09.

Conclusion

Understanding and calculating simple and compound interest is crucial for financial planning and investment. By applying the appropriate formulas and steps, you can accurately determine how much interest you will earn or be charged over a specific period.

For more detailed calculations and personalized investment advice, consider using financial calculators or consulting with a financial advisor. Remember, the key to success in finance lies in informed decisions and accurate calculations.